Mesh not moving with armature
Your object is not weight painted. Blender needs to know which vertices are influenced by which bone. This is done by painting weights
Basically you can do that two ways:
1 - Parent your mesh to your armature with automatic weights. You may have to tweak things as explained in point 2 though
2 - select a bone of your armature and go to weight paint mode to paint (red) the vertices influenced by that bone. Repeat for each bone.

Also make sure "deform" is ticked as shown on the picture, without which your bones will have no influence on your mesh.